This is a multicenter double-blind, randomized, placebo-controlled parallel study with a rescue phase to evaluate the efficacy and safety of caffeine citrate in the treatment of apnea of prematurity. The primary evaluable endpoint is a 50% decrease in the frequency of apnea spells. A sample size of 75 patients has been chosen based upon the assumption that success among caffeine-treated patients will be 70% or more and 20% or less success in the placebo group. The double-blind phase will last a minimum of 48 hours.